NOMBRES - Curiosités, théorie et usages

 

Accueil                           DicoNombre            Rubriques           Nouveautés      Édition du: 21/04/2020

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PARTITIONS

 

Débutants

Addition

PARTITIONS STRICTES

 

Glossaire

Addition

 

INDEX

Partition

Calculs

 

Partitions strictes

Table des partitions strictes

Fonction génératrice

Quantité de partitions strictes

 

Sommaire de cette page

>>> Liste des partitions strictes pour n de 1 à 25

>>> Liste des partitions impaires pour n de 1 à 15

>>> Exemples de partitions strictes avec multiples de 5, 7 et 11

 

 

PARTITIONS STRICTES

TABLE

 Voir Partitions des nombres de 1 à 10

Quantité de partitions strictes ou impaires

 

 

Liste des partitions strictes pour n de 1 à 25

 

Exemple

5, 7, 3, [[2, 3], [1, 4], [5]]

 

 

Le nombre 5 peut être exprimé avec 7 sommes de nombres (partitions) dont 3 sont faites de nombres distincts (partitions strictes).

Ce sont: 2 + 3, 1 + 4 et 5.

 

 

1, 1, 1, [[1]]

2, 2, 1, [[2]]

3, 3, 2, [[1, 2], [3]]

4, 5, 2, [[1, 3], [4]]

5, 7, 3, [[2, 3], [1, 4], [5]]

6, 11, 4, [[1, 2, 3], [2, 4], [1, 5], [6]]

7, 15, 5, [[1, 2, 4], [3, 4], [2, 5], [1, 6], [7]]

8, 22, 6, [[1, 3, 4], [1, 2, 5], [3, 5], [2, 6], [1, 7], [8]]

9, 30, 8, [[2, 3, 4], [1, 3, 5], [4, 5], [1, 2, 6], [3, 6], [2, 7], [1, 8], [9]]

10, 42, 10, [[1, 2, 3, 4], [2, 3, 5], [1, 4, 5], [1, 3, 6], [4, 6], [1, 2, 7], [3, 7], [2, 8], [1, 9], [10]]

11, 56, 12, [[1, 2, 3, 5], [2, 4, 5], [2, 3, 6], [1, 4, 6], [5, 6], [1, 3, 7], [4, 7], [1, 2, 8], [3, 8], [2, 9], [1, 10], [11]]

12, 77, 15, [[1, 2, 4, 5], [3, 4, 5], [1, 2, 3, 6], [2, 4, 6], [1, 5, 6], [2, 3, 7], [1, 4, 7], [5, 7], [1, 3, 8], [4, 8], [1, 2, 9], [3, 9], [2, 10], [1, 11], [12]]

13, 101, 18, [[1, 3, 4, 5], [1, 2, 4, 6], [3, 4, 6], [2, 5, 6], [1, 2, 3, 7], [2, 4, 7], [1, 5, 7], [6, 7], [2, 3, 8], [1, 4, 8], [5, 8], [1, 3, 9], [4, 9], [1, 2, 10], [3, 10], [2, 11], [1, 12], [13]]

14, 135, 22, [[2, 3, 4, 5], [1, 3, 4, 6], [1, 2, 5, 6], [3, 5, 6], [1, 2, 4, 7], [3, 4, 7], [2, 5, 7], [1, 6, 7], [1, 2, 3, 8], [2, 4, 8], [1, 5, 8], [6, 8], [2, 3, 9], [1, 4, 9], [5, 9], [1, 3, 10], [4, 10], [1, 2, 11], [3, 11], [2, 12], [1, 13], [14]]

15, 176, 27, [[1, 2, 3, 4, 5], [2, 3, 4, 6], [1, 3, 5, 6], [4, 5, 6], [1, 3, 4, 7], [1, 2, 5, 7], [3, 5, 7], [2, 6, 7], [1, 2, 4, 8], [3, 4, 8], [2, 5, 8], [1, 6, 8], [7, 8], [1, 2, 3, 9], [2, 4, 9], [1, 5, 9], [6, 9], [2, 3, 10], [1, 4, 10], [5, 10], [1, 3, 11], [4, 11], [1, 2, 12], [3, 12], [2, 13], [1, 14], [15]]

16, 231, 32, [[1, 2, 3, 4, 6], [2, 3, 5, 6], [1, 4, 5, 6], [2, 3, 4, 7], [1, 3, 5, 7], [4, 5, 7], [1, 2, 6, 7], [3, 6, 7], [1, 3, 4, 8], [1, 2, 5, 8], [3, 5, 8], [2, 6, 8], [1, 7, 8], [1, 2, 4, 9], [3, 4, 9], [2, 5, 9], [1, 6, 9], [7, 9], [1, 2, 3, 10], [2, 4, 10], [1, 5, 10], [6, 10], [2, 3, 11], [1, 4, 11], [5, 11], [1, 3, 12], [4, 12], [1, 2, 13], [3, 13], [2, 14], [1, 15], [16]]

17, 297, 38, [[1, 2, 3, 5, 6], [2, 4, 5, 6], [1, 2, 3, 4, 7], [2, 3, 5, 7], [1, 4, 5, 7], [1, 3, 6, 7], [4, 6, 7], [2, 3, 4, 8], [1, 3, 5, 8], [4, 5, 8], [1, 2, 6, 8], [3, 6, 8], [2, 7, 8], [1, 3, 4, 9], [1, 2, 5, 9], [3, 5, 9], [2, 6, 9], [1, 7, 9], [8, 9], [1, 2, 4, 10], [3, 4, 10], [2, 5, 10], [1, 6, 10], [7, 10], [1, 2, 3, 11], [2, 4, 11], [1, 5, 11], [6, 11], [2, 3, 12], [1, 4, 12], [5, 12], [1, 3, 13], [4, 13], [1, 2, 14], [3, 14], [2, 15], [1, 16], [17]]

18, 385, 46, [[1, 2, 4, 5, 6], [3, 4, 5, 6], [1, 2, 3, 5, 7], [2, 4, 5, 7], [2, 3, 6, 7], [1, 4, 6, 7], [5, 6, 7], [1, 2, 3, 4, 8], [2, 3, 5, 8], [1, 4, 5, 8], [1, 3, 6, 8], [4, 6, 8], [1, 2, 7, 8], [3, 7, 8], [2, 3, 4, 9], [1, 3, 5, 9], [4, 5, 9], [1, 2, 6, 9], [3, 6, 9], [2, 7, 9], [1, 8, 9], [1, 3, 4, 10], [1, 2, 5, 10], [3, 5, 10], [2, 6, 10], [1, 7, 10], [8, 10], [1, 2, 4, 11], [3, 4, 11], [2, 5, 11], [1, 6, 11], [7, 11], [1, 2, 3, 12], [2, 4, 12], [1, 5, 12], [6, 12], [2, 3, 13], [1, 4, 13], [5, 13], [1, 3, 14], [4, 14], [1, 2, 15], [3, 15], [2, 16], [1, 17], [18]]

19, 490, 54, [[1, 3, 4, 5, 6], [1, 2, 4, 5, 7], [3, 4, 5, 7], [1, 2, 3, 6, 7], [2, 4, 6, 7], [1, 5, 6, 7], [1, 2, 3, 5, 8], [2, 4, 5, 8], [2, 3, 6, 8], [1, 4, 6, 8], [5, 6, 8], [1, 3, 7, 8], [4, 7, 8], [1, 2, 3, 4, 9], [2, 3, 5, 9], [1, 4, 5, 9], [1, 3, 6, 9], [4, 6, 9], [1, 2, 7, 9], [3, 7, 9], [2, 8, 9], [2, 3, 4, 10], [1, 3, 5, 10], [4, 5, 10], [1, 2, 6, 10], [3, 6, 10], [2, 7, 10], [1, 8, 10], [9, 10], [1, 3, 4, 11], [1, 2, 5, 11], [3, 5, 11], [2, 6, 11], [1, 7, 11], [8, 11], [1, 2, 4, 12], [3, 4, 12], [2, 5, 12], [1, 6, 12], [7, 12], [1, 2, 3, 13], [2, 4, 13], [1, 5, 13], [6, 13], [2, 3, 14], [1, 4, 14], [5, 14], [1, 3, 15], [4, 15], [1, 2, 16], [3, 16], [2, 17], [1, 18], [19]]

20, 627, 64, [[2, 3, 4, 5, 6], [1, 3, 4, 5, 7], [1, 2, 4, 6, 7], [3, 4, 6, 7], [2, 5, 6, 7], [1, 2, 4, 5, 8], [3, 4, 5, 8], [1, 2, 3, 6, 8], [2, 4, 6, 8], [1, 5, 6, 8], [2, 3, 7, 8], [1, 4, 7, 8], [5, 7, 8], [1, 2, 3, 5, 9], [2, 4, 5, 9], [2, 3, 6, 9], [1, 4, 6, 9], [5, 6, 9], [1, 3, 7, 9], [4, 7, 9], [1, 2, 8, 9], [3, 8, 9], [1, 2, 3, 4, 10], [2, 3, 5, 10], [1, 4, 5, 10], [1, 3, 6, 10], [4, 6, 10], [1, 2, 7, 10], [3, 7, 10], [2, 8, 10], [1, 9, 10], [2, 3, 4, 11], [1, 3, 5, 11], [4, 5, 11], [1, 2, 6, 11], [3, 6, 11], [2, 7, 11], [1, 8, 11], [9, 11], [1, 3, 4, 12], [1, 2, 5, 12], [3, 5, 12], [2, 6, 12], [1, 7, 12], [8, 12], [1, 2, 4, 13], [3, 4, 13], [2, 5, 13], [1, 6, 13], [7, 13], [1, 2, 3, 14], [2, 4, 14], [1, 5, 14], [6, 14], [2, 3, 15], [1, 4, 15], [5, 15], [1, 3, 16], [4, 16], [1, 2, 17], [3, 17], [2, 18], [1, 19], [20]]

21, 792, 76, [[1, 2, 3, 4, 5, 6], [2, 3, 4, 5, 7], [1, 3, 4, 6, 7], [1, 2, 5, 6, 7], [3, 5, 6, 7], [1, 3, 4, 5, 8], [1, 2, 4, 6, 8], [3, 4, 6, 8], [2, 5, 6, 8], [1, 2, 3, 7, 8], [2, 4, 7, 8], [1, 5, 7, 8], [6, 7, 8], [1, 2, 4, 5, 9], [3, 4, 5, 9], [1, 2, 3, 6, 9], [2, 4, 6, 9], [1, 5, 6, 9], [2, 3, 7, 9], [1, 4, 7, 9], [5, 7, 9], [1, 3, 8, 9], [4, 8, 9], [1, 2, 3, 5, 10], [2, 4, 5, 10], [2, 3, 6, 10], [1, 4, 6, 10], [5, 6, 10], [1, 3, 7, 10], [4, 7, 10], [1, 2, 8, 10], [3, 8, 10], [2, 9, 10], [1, 2, 3, 4, 11], [2, 3, 5, 11], [1, 4, 5, 11], [1, 3, 6, 11], [4, 6, 11], [1, 2, 7, 11], [3, 7, 11], [2, 8, 11], [1, 9, 11], [10, 11], [2, 3, 4, 12], [1, 3, 5, 12], [4, 5, 12], [1, 2, 6, 12], [3, 6, 12], [2, 7, 12], [1, 8, 12], [9, 12], [1, 3, 4, 13], [1, 2, 5, 13], [3, 5, 13], [2, 6, 13], [1, 7, 13], [8, 13], [1, 2, 4, 14], [3, 4, 14], [2, 5, 14], [1, 6, 14], [7, 14], [1, 2, 3, 15], [2, 4, 15], [1, 5, 15], [6, 15], [2, 3, 16], [1, 4, 16], [5, 16], [1, 3, 17], [4, 17], [1, 2, 18], [3, 18], [2, 19], [1, 20], [21]]

22, 1002, 89, [[1, 2, 3, 4, 5, 7], [2, 3, 4, 6, 7], [1, 3, 5, 6, 7], [4, 5, 6, 7], [2, 3, 4, 5, 8], [1, 3, 4, 6, 8], [1, 2, 5, 6, 8], [3, 5, 6, 8], [1, 2, 4, 7, 8], [3, 4, 7, 8], [2, 5, 7, 8], [1, 6, 7, 8], [1, 3, 4, 5, 9], [1, 2, 4, 6, 9], [3, 4, 6, 9], [2, 5, 6, 9], [1, 2, 3, 7, 9], [2, 4, 7, 9], [1, 5, 7, 9], [6, 7, 9], [2, 3, 8, 9], [1, 4, 8, 9], [5, 8, 9], [1, 2, 4, 5, 10], [3, 4, 5, 10], [1, 2, 3, 6, 10], [2, 4, 6, 10], [1, 5, 6, 10], [2, 3, 7, 10], [1, 4, 7, 10], [5, 7, 10], [1, 3, 8, 10], [4, 8, 10], [1, 2, 9, 10], [3, 9, 10], [1, 2, 3, 5, 11], [2, 4, 5, 11], [2, 3, 6, 11], [1, 4, 6, 11], [5, 6, 11], [1, 3, 7, 11], [4, 7, 11], [1, 2, 8, 11], [3, 8, 11], [2, 9, 11], [1, 10, 11], [1, 2, 3, 4, 12], [2, 3, 5, 12], [1, 4, 5, 12], [1, 3, 6, 12], [4, 6, 12], [1, 2, 7, 12], [3, 7, 12], [2, 8, 12], [1, 9, 12], [10, 12], [2, 3, 4, 13], [1, 3, 5, 13], [4, 5, 13], [1, 2, 6, 13], [3, 6, 13], [2, 7, 13], [1, 8, 13], [9, 13], [1, 3, 4, 14], [1, 2, 5, 14], [3, 5, 14], [2, 6, 14], [1, 7, 14], [8, 14], [1, 2, 4, 15], [3, 4, 15], [2, 5, 15], [1, 6, 15], [7, 15], [1, 2, 3, 16], [2, 4, 16], [1, 5, 16], [6, 16], [2, 3, 17], [1, 4, 17], [5, 17], [1, 3, 18], [4, 18], [1, 2, 19], [3, 19], [2, 20], [1, 21], [22]]

23, 1255, 104, [[1, 2, 3, 4, 6, 7], [2, 3, 5, 6, 7], [1, 4, 5, 6, 7], [1, 2, 3, 4, 5, 8], [2, 3, 4, 6, 8], [1, 3, 5, 6, 8], [4, 5, 6, 8], [1, 3, 4, 7, 8], [1, 2, 5, 7, 8], [3, 5, 7, 8], [2, 6, 7, 8], [2, 3, 4, 5, 9], [1, 3, 4, 6, 9], [1, 2, 5, 6, 9], [3, 5, 6, 9], [1, 2, 4, 7, 9], [3, 4, 7, 9], [2, 5, 7, 9], [1, 6, 7, 9], [1, 2, 3, 8, 9], [2, 4, 8, 9], [1, 5, 8, 9], [6, 8, 9], [1, 3, 4, 5, 10], [1, 2, 4, 6, 10], [3, 4, 6, 10], [2, 5, 6, 10], [1, 2, 3, 7, 10], [2, 4, 7, 10], [1, 5, 7, 10], [6, 7, 10], [2, 3, 8, 10], [1, 4, 8, 10], [5, 8, 10], [1, 3, 9, 10], [4, 9, 10], [1, 2, 4, 5, 11], [3, 4, 5, 11], [1, 2, 3, 6, 11], [2, 4, 6, 11], [1, 5, 6, 11], [2, 3, 7, 11], [1, 4, 7, 11], [5, 7, 11], [1, 3, 8, 11], [4, 8, 11], [1, 2, 9, 11], [3, 9, 11], [2, 10, 11], [1, 2, 3, 5, 12], [2, 4, 5, 12], [2, 3, 6, 12], [1, 4, 6, 12], [5, 6, 12], [1, 3, 7, 12], [4, 7, 12], [1, 2, 8, 12], [3, 8, 12], [2, 9, 12], [1, 10, 12], [11, 12], [1, 2, 3, 4, 13], [2, 3, 5, 13], [1, 4, 5, 13], [1, 3, 6, 13], [4, 6, 13], [1, 2, 7, 13], [3, 7, 13], [2, 8, 13], [1, 9, 13], [10, 13], [2, 3, 4, 14], [1, 3, 5, 14], [4, 5, 14], [1, 2, 6, 14], [3, 6, 14], [2, 7, 14], [1, 8, 14], [9, 14], [1, 3, 4, 15], [1, 2, 5, 15], [3, 5, 15], [2, 6, 15], [1, 7, 15], [8, 15], [1, 2, 4, 16], [3, 4, 16], [2, 5, 16], [1, 6, 16], [7, 16], [1, 2, 3, 17], [2, 4, 17], [1, 5, 17], [6, 17], [2, 3, 18], [1, 4, 18], [5, 18], [1, 3, 19], [4, 19], [1, 2, 20], [3, 20], [2, 21], [1, 22], [23]]

24, 1575, 122, [[1, 2, 3, 5, 6, 7], [2, 4, 5, 6, 7], [1, 2, 3, 4, 6, 8], [2, 3, 5, 6, 8], [1, 4, 5, 6, 8], [2, 3, 4, 7, 8], [1, 3, 5, 7, 8], [4, 5, 7, 8], [1, 2, 6, 7, 8], [3, 6, 7, 8], [1, 2, 3, 4, 5, 9], [2, 3, 4, 6, 9], [1, 3, 5, 6, 9], [4, 5, 6, 9], [1, 3, 4, 7, 9], [1, 2, 5, 7, 9], [3, 5, 7, 9], [2, 6, 7, 9], [1, 2, 4, 8, 9], [3, 4, 8, 9], [2, 5, 8, 9], [1, 6, 8, 9], [7, 8, 9], [2, 3, 4, 5, 10], [1, 3, 4, 6, 10], [1, 2, 5, 6, 10], [3, 5, 6, 10], [1, 2, 4, 7, 10], [3, 4, 7, 10], [2, 5, 7, 10], [1, 6, 7, 10], [1, 2, 3, 8, 10], [2, 4, 8, 10], [1, 5, 8, 10], [6, 8, 10], [2, 3, 9, 10], [1, 4, 9, 10], [5, 9, 10], [1, 3, 4, 5, 11], [1, 2, 4, 6, 11], [3, 4, 6, 11], [2, 5, 6, 11], [1, 2, 3, 7, 11], [2, 4, 7, 11], [1, 5, 7, 11], [6, 7, 11], [2, 3, 8, 11], [1, 4, 8, 11], [5, 8, 11], [1, 3, 9, 11], [4, 9, 11], [1, 2, 10, 11], [3, 10, 11], [1, 2, 4, 5, 12], [3, 4, 5, 12], [1, 2, 3, 6, 12], [2, 4, 6, 12], [1, 5, 6, 12], [2, 3, 7, 12], [1, 4, 7, 12], [5, 7, 12], [1, 3, 8, 12], [4, 8, 12], [1, 2, 9, 12], [3, 9, 12], [2, 10, 12], [1, 11, 12], [1, 2, 3, 5, 13], [2, 4, 5, 13], [2, 3, 6, 13], [1, 4, 6, 13], [5, 6, 13], [1, 3, 7, 13], [4, 7, 13], [1, 2, 8, 13], [3, 8, 13], [2, 9, 13], [1, 10, 13], [11, 13], [1, 2, 3, 4, 14], [2, 3, 5, 14], [1, 4, 5, 14], [1, 3, 6, 14], [4, 6, 14], [1, 2, 7, 14], [3, 7, 14], [2, 8, 14], [1, 9, 14], [10, 14], [2, 3, 4, 15], [1, 3, 5, 15], [4, 5, 15], [1, 2, 6, 15], [3, 6, 15], [2, 7, 15], [1, 8, 15], [9, 15], [1, 3, 4, 16], [1, 2, 5, 16], [3, 5, 16], [2, 6, 16], [1, 7, 16], [8, 16], [1, 2, 4, 17], [3, 4, 17], [2, 5, 17], [1, 6, 17], [7, 17], [1, 2, 3, 18], [2, 4, 18], [1, 5, 18], [6, 18], [2, 3, 19], [1, 4, 19], [5, 19], [1, 3, 20], [4, 20], [1, 2, 21], [3, 21], [2, 22], [1, 23], [24]]

25, 1958, 142, [[1, 2, 4, 5, 6, 7], [3, 4, 5, 6, 7], [1, 2, 3, 5, 6, 8], [2, 4, 5, 6, 8], [1, 2, 3, 4, 7, 8], [2, 3, 5, 7, 8], [1, 4, 5, 7, 8], [1, 3, 6, 7, 8], [4, 6, 7, 8], [1, 2, 3, 4, 6, 9], [2, 3, 5, 6, 9], [1, 4, 5, 6, 9], [2, 3, 4, 7, 9], [1, 3, 5, 7, 9], [4, 5, 7, 9], [1, 2, 6, 7, 9], [3, 6, 7, 9], [1, 3, 4, 8, 9], [1, 2, 5, 8, 9], [3, 5, 8, 9], [2, 6, 8, 9], [1, 7, 8, 9], [1, 2, 3, 4, 5, 10], [2, 3, 4, 6, 10], [1, 3, 5, 6, 10], [4, 5, 6, 10], [1, 3, 4, 7, 10], [1, 2, 5, 7, 10], [3, 5, 7, 10], [2, 6, 7, 10], [1, 2, 4, 8, 10], [3, 4, 8, 10], [2, 5, 8, 10], [1, 6, 8, 10], [7, 8, 10], [1, 2, 3, 9, 10], [2, 4, 9, 10], [1, 5, 9, 10], [6, 9, 10], [2, 3, 4, 5, 11], [1, 3, 4, 6, 11], [1, 2, 5, 6, 11], [3, 5, 6, 11], [1, 2, 4, 7, 11], [3, 4, 7, 11], [2, 5, 7, 11], [1, 6, 7, 11], [1, 2, 3, 8, 11], [2, 4, 8, 11], [1, 5, 8, 11], [6, 8, 11], [2, 3, 9, 11], [1, 4, 9, 11], [5, 9, 11], [1, 3, 10, 11], [4, 10, 11], [1, 3, 4, 5, 12], [1, 2, 4, 6, 12], [3, 4, 6, 12], [2, 5, 6, 12], [1, 2, 3, 7, 12], [2, 4, 7, 12], [1, 5, 7, 12], [6, 7, 12], [2, 3, 8, 12], [1, 4, 8, 12], [5, 8, 12], [1, 3, 9, 12], [4, 9, 12], [1, 2, 10, 12], [3, 10, 12], [2, 11, 12], [1, 2, 4, 5, 13], [3, 4, 5, 13], [1, 2, 3, 6, 13], [2, 4, 6, 13], [1, 5, 6, 13], [2, 3, 7, 13], [1, 4, 7, 13], [5, 7, 13], [1, 3, 8, 13], [4, 8, 13], [1, 2, 9, 13], [3, 9, 13], [2, 10, 13], [1, 11, 13], [12, 13], [1, 2, 3, 5, 14], [2, 4, 5, 14], [2, 3, 6, 14], [1, 4, 6, 14], [5, 6, 14], [1, 3, 7, 14], [4, 7, 14], [1, 2, 8, 14], [3, 8, 14], [2, 9, 14], [1, 10, 14], [11, 14], [1, 2, 3, 4, 15], [2, 3, 5, 15], [1, 4, 5, 15], [1, 3, 6, 15], [4, 6, 15], [1, 2, 7, 15], [3, 7, 15], [2, 8, 15], [1, 9, 15], [10, 15], [2, 3, 4, 16], [1, 3, 5, 16], [4, 5, 16], [1, 2, 6, 16], [3, 6, 16], [2, 7, 16], [1, 8, 16], [9, 16], [1, 3, 4, 17], [1, 2, 5, 17], [3, 5, 17], [2, 6, 17], [1, 7, 17], [8, 17], [1, 2, 4, 18], [3, 4, 18], [2, 5, 18], [1, 6, 18], [7, 18], [1, 2, 3, 19], [2, 4, 19], [1, 5, 19], [6, 19], [2, 3, 20], [1, 4, 20], [5, 20], [1, 3, 21], [4, 21], [1, 2, 22], [3, 22], [2, 23], [1, 24], [25]]

 

 

Liste des partitions impaires pour n de 1 à 15

 

Exemple

5, 7, 3, [[2, 3], [1, 4], [5]]

 

 

Le nombre 5 peut être exprimé avec 7 sommes de nombres (partitions) dont 3 sont faites de nombres imapirs (partitions impaires).

Ce sont: 1+1+1+1+1, 1+1+3 et 5

 

1, 1, 1, [[1]]

2, 2, 1, [[1, 1]]

3, 3, 2, [[1, 1, 1], [3]]

4, 5, 2, [[1, 1, 1, 1], [1, 3]]

5, 7, 3, [[1, 1, 1, 1, 1], [1, 1, 3], [5]]

6, 11, 4, [[1, 1, 1, 1, 1, 1], [1, 1, 1, 3], [3, 3], [1, 5]]

7, 15, 5, [[1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 3], [1, 3, 3], [1, 1, 5], [7]]

8, 22, 6, [[1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 3], [1, 1, 3, 3], [1, 1, 1, 5], [3, 5], [1, 7]]

9, 30, 8, [[1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 3], [1, 1, 1, 3, 3], [3, 3, 3], [1, 1, 1, 1, 5], [1, 3, 5], [1, 1, 7], [9]]

10, 42, 10, [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 3], [1, 1, 1, 1, 3, 3], [1, 3, 3, 3], [1, 1, 1, 1, 1, 5], [1, 1, 3, 5], [5, 5], [1, 1, 1, 7], [3, 7], [1, 9]]

11, 56, 12, [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 3], [1, 1, 1, 1, 1, 3, 3], [1, 1, 3, 3, 3], [1, 1, 1, 1, 1, 1, 5], [1, 1, 1, 3, 5], [3, 3, 5], [1, 5, 5], [1, 1, 1, 1, 7], [1, 3, 7], [1, 1, 9], [11]]

12, 77, 15, [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3], [1, 1, 1, 1, 1, 1, 3, 3], [1, 1, 1, 3, 3, 3], [3, 3, 3, 3], [1, 1, 1, 1, 1, 1, 1, 5], [1, 1, 1, 1, 3, 5], [1, 3, 3, 5], [1, 1, 5, 5], [1, 1, 1, 1, 1, 7], [1, 1, 3, 7], [5, 7], [1, 1, 1, 9], [3, 9], [1, 11]]

13, 101, 18, [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3], [1, 1, 1, 1, 1, 1, 1, 3, 3], [1, 1, 1, 1, 3, 3, 3], [1, 3, 3, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 5], [1, 1, 1, 1, 1, 3, 5], [1, 1, 3, 3, 5], [1, 1, 1, 5, 5], [3, 5, 5], [1, 1, 1, 1, 1, 1, 7], [1, 1, 1, 3, 7], [3, 3, 7], [1, 5, 7], [1, 1, 1, 1, 9], [1, 3, 9], [1, 1, 11], [13]]

14, 135, 22, [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3], [1, 1, 1, 1, 1, 1, 1, 1, 3, 3], [1, 1, 1, 1, 1, 3, 3, 3], [1, 1, 3, 3, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 5], [1, 1, 1, 1, 1, 1, 3, 5], [1, 1, 1, 3, 3, 5], [3, 3, 3, 5], [1, 1, 1, 1, 5, 5], [1, 3, 5, 5], [1, 1, 1, 1, 1, 1, 1, 7], [1, 1, 1, 1, 3, 7], [1, 3, 3, 7], [1, 1, 5, 7], [7, 7], [1, 1, 1, 1, 1, 9], [1, 1, 3, 9], [5, 9], [1, 1, 1, 11], [3, 11], [1, 13]]

15, 176, 27, [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3], [1, 1, 1, 1, 1, 1, 3, 3, 3], [1, 1, 1, 3, 3, 3, 3], [3, 3, 3, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5], [1, 1, 1, 1, 1, 1, 1, 3, 5], [1, 1, 1, 1, 3, 3, 5], [1, 3, 3, 3, 5], [1, 1, 1, 1, 1, 5, 5], [1, 1, 3, 5, 5], [5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 7], [1, 1, 1, 1, 1, 3, 7], [1, 1, 3, 3, 7], [1, 1, 1, 5, 7], [3, 5, 7], [1, 7, 7], [1, 1, 1, 1, 1, 1, 9], [1, 1, 1, 3, 9], [3, 3, 9], [1, 5, 9], [1, 1, 1, 1, 11], [1, 3, 11], [1, 1, 13], [15]]

 

 

Exemples de partitions strictes

avec multiples de 5, 7 et 11

S = a + b + c          a             b             c

 23                           5            7            11

 30                           5            14          11

 34                           5            7            22

 37                           5            21          11

 38                           20          7            11

 41                           5            14          22

 44                           5            28          11

 45                           20          14          11

 45                           5            7            33

 48                           5            21          22

 49                           20          7            22

 52                           20          21          11

 52                           5            14          33

 53                           35          7            11

 55                           5            28          22

 56                           20          14          22

 59                           20          28          11

 59                           5            21          33

 60                           35          14          11

 60                           20          7            33

 63                           20          21          22

 64                           35          7            22

 66                           5            28          33

 67                           35          21          11

 67                           20          14          33

 70                           20          28          22

 71                           35          14          22

 74                           35          28          11

 74                           20          21          33

 75                           35          7            33

 78                           35          21          22

 81                           20          28          33

 82                           35          14          33

 85                           35          28          22

 89                           35          21          33

 96                           35          28          33

 

 

  

Retour

*    Partitions strictes

Suite

*    Partitions – Index

*    Digi-Partition

*   Partition sous contraintes

Voir

*    Addition - Glossaire

*    Addition des carrés

*    Addition des entiers

*    Addition des puissances

*    Carrés magiques

*    Conjecture de Goldbach

*    La magie du carré 3 x3

*    Multi-somme de puissances

*    Partition de 15

*    S'y retrouver

*    Totient d'Euler

Sites

*      Partition function Q – Wolfram MathWorld

*    OEIS A000009 - Expansion of Product_{m >= 1} (1 + x^m); number of partitions of n into distinct parts; number of partitions of n into odd parts

Cette page

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